You can save your function definition in a notebook .nb file and load that notebook before beginning the next time.

Just loading that notebook will not automatically evaluate your definition, you must again evaluate the definition for Mathematica to use the definition.

It is possible, if this is a definition that you will want to use every time to modify the properties of the cell to make Mathematica automatically evaluate that cell with your fuction definition every time you load the notebook. That is documented here.